SESSION 1A FUNCTIONAL MATERIALS I - Eawag-Empa Library
SESSION 1A FUNCTIONAL MATERIALS I - Eawag-Empa Library
SESSION 1A FUNCTIONAL MATERIALS I - Eawag-Empa Library
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Biomimetics in airship design<br />
19 th International Conference on<br />
Adaptive Structures and Technologies<br />
October 6-9, 2008<br />
Ascona, Switzerland<br />
S. Michel 1 *, Ch. Jordi 1 , L. Wahl 2 , N. Widmer 2 , Erich Fink 3 , L. Kniese 4 and A. Bormann 5<br />
1 Swiss Federal Laboratories for Materials Testing and Research (<strong>Empa</strong>), Duebendorf, Switzerland,<br />
2 Swiss Federal Institute of technology, Zuerich, Switzerland,<br />
3 Technical University Berlin, Berlin, Germany,<br />
4 Evologics GmbH, Berlin, Germany,<br />
5 AeroiX GmbH, Kleinmachnow, Germany.<br />
* Corresponding author: S. Michel, Ueberlandstrasse 129, CH-8600 Duebendorf, Switzerland<br />
Tel: +41 - (0)44 823 45 88, Fax: +41 - (0)44 823 40 11, E-mail: silvain.michel@empa.ch<br />
ABSTRACT<br />
Many attempts have been made to mimic the movement of a fish in water in order to find<br />
novel solutions in autonomous underwater vehicles (AUV) [1-4]. Conventional airships are driven by<br />
propellers and steered by stabilizers with rudders or with thrust vector control. Such propulsion and<br />
steering systems are efficient only in a small range of operation. The goal of our project is to mimic<br />
the fish-like movement with an airship body in air. In a theoretical study [5] we have shown that a 6m<br />
long airship in air is similar to the trout in water. Therefore we want to build a geometrically similar<br />
body which mimics the body motion of a trout in steady state swimming. The activation is realized<br />
using Dielectric Elastomers (DE), a promising class of Electroactive Polymers (EAP). The principles<br />
of biomimetics in structural design and propulsion are discussed in this paper. The similarity of the<br />
optimized solutions found by the evolution for animals living in water and an optimized design of an<br />
airship will be shown. In a next step, the design of an indoor-flying airship propelled by a fish-like<br />
motion is evaluated. Various development tests, including wind tunnel testing and flight trials were<br />
performed and the gained results will be presented. First computational fluiddynamic simulations<br />
performed have shown similar vortex flow fields. In addition, the average forces could be measured<br />
accurately in wind tunnel tests and will be used to dimensioning the activation of the fin<br />
appropriately. From these results a conclusion shall be drawn, how far biomimetics can be used<br />
successfully in the design of future airship.<br />
Keywords: Biomimetics, airship, active structures, electroactive polymers, dielectric elastomers<br />
1. INTRODUCTION<br />
Lighter-Than-Air vehicles are a promising class of transport systems for heavy cargo,<br />
stratospheric platforms, but also for surveillance or animal observations. In the last decades various<br />
concept studies have been performed for stratospheric platforms, which are interesting alternatives<br />
for land-based networks as well as for satellites in telecommunication, reconnaissance and<br />
observation [6-10]. Classical propulsion systems composed of piston engines with gears and<br />
propellers show a limited efficiency due to thermo mechanical losses in the engine, mechanical losses<br />
in the gears and fluid dynamical restrictions of the propellers. In addition these systems are noisy and<br />
if driven by piston engine have a negative impact on the environment by pollution. These<br />
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disadvantages can be grave, for they prohibit some new applications such as stratospheric platforms<br />
(energy efficiency) [10], animal observations or surveillance (noise). New systems should be energy<br />
efficient, noiseless and environmentally friendly. Our idea in this context is to apply biomimetic<br />
principles.<br />
2. THEORETICAL FEASABILITY<br />
The method of mimicking biological forms and concepts in the development of technical<br />
products has a long tradition. A pioneer in biomimetic aerospace design was Hertel, who already in<br />
1963 was studying natural forms of various fishes for efficient fuselage designs and alternative<br />
propulsion systems for airplanes [11]. Later Bannasch for example analyzed in detail living penguins<br />
and their bodies, which have an extraordinary low drag coefficient [12, 13]. His results were first used<br />
for an airship design by the Technical University of Berlin in 1998 in the airship called “Luftfisch”.<br />
The shape of this 10m long semi-rigid airship is basically a rotational symmetric shape of a penguin.<br />
We went one step further, when we suggested not only to adapt the form of a fish (in order to reduce<br />
the drag), but also its motion as an efficient propulsion system [5, 14]. The main motivation for such<br />
a new concept for the propulsion of an airship is its much better efficiency.<br />
2-1. Propulsion Efficiency Considerations<br />
Considering a conventional propeller driven rigid airship (Fig. 1), the thrust is generated quite<br />
inefficiently by propellers that are mounted sidewise of the body. The size of the propellers’<br />
diameters is fairly limited to avoid supersonic relative tip mach numbers. Consequently, the air has to<br />
be accelerated quite significantly in order to generate enough momentum to compensate the drag due<br />
to body friction and the wake behind the airship in case of boundary layer separation. The momentum<br />
which is produced by a propeller and the momentum loss induced by the flow resistance of the airship<br />
body can be calculated with following equations [11]:<br />
<br />
<br />
FT ( uT uT<br />
u0<br />
<br />
(1.a)<br />
FR ( uR uR<br />
u0<br />
<br />
(1.b)<br />
The reason for the low efficiency of these kind of thrust generation is the high velocity of the<br />
propeller air jet uT.<br />
Figure 1. Schematically sketched rigid airship with conventional propulsion by propellers.
Figure 2. Schematically sketched fish with propulsion by undulating body motion and fin stroke.<br />
In case of a swimming fish (Fig. 2) the thrust is generated by body undulation and/or by<br />
caudal fin flapping. The major advantage of this propulsion concept is that thrust is generated at the<br />
same location where body induced momentum loss occurs. The rigid fish body causes a wake flow<br />
which is in direct correlation to momentum loss (Eq. 1.b). In order to obtain a trust at constant speed,<br />
this momentum loss has to be compensated by the propulsion mechanism. Consequently, in this case<br />
there is no relative velocity between the flow behind the fish body and the surrounding fluid, which<br />
manifests in a vortex line that is fixed in space. Hertel [11] conducted a thought experiment to<br />
illustrate the efficiency advantage of fish-like propulsion. There are two different configurations to<br />
compensate a momentum loss of a flow caused by resistance. The first possibility is to use a thrust<br />
generator (propeller) in parallel with the decelerated fluid. The other way is to set it in series. He<br />
verifies his statement that the required power is reduced if the locations of momentum loss and thrust<br />
generation fall into one another with following calculations:<br />
P F u u ) / 2 (in parallel configuration) (2.a)<br />
p<br />
R ( 0 T<br />
P F u u ) / 2 (in series configuration) (2.b)<br />
S<br />
R ( 0 R<br />
In the first configuration, the propeller has to accelerate the fluid from u0 up to uT in order to<br />
compensate the momentum loss. In the second configuration, after deceleration of the fluid to uR, it is<br />
accelerated up to u0 again. It is obvious, that uR is smaller than uT. Therefore PS is smaller than PP as<br />
well. Hertel [11] predicted a power reduction of up to 60%. In Fig. 3, which is adapted from Fish and<br />
Lauder [15] the propulsive efficiencies of a marine propeller and different whales are compared.<br />
It shows that the efficiency of fish-like locomotion is significantly higher and also for a broad<br />
range of thrust coefficient almost constant. The propeller system has only at one specific thrust<br />
coefficient a maximum and decays drastically to both sides of the maximum. These interesting<br />
findings are not only valid in water, but when correctly transformed also in air.<br />
If the shape and motion of swimming fish in water is to be transferred to an airship in air,<br />
fluiddynamic similarity theorem has to be considered.
Figure 3. Comparison of relationships of propulsive efficiency and thrust coefficient for 4 species of small whales and a<br />
typical marine propeller [15].<br />
2-2. Similarity and dimensional analysis<br />
In the following analysis we assume a 6 meter long airship flying with a steady state velocity<br />
of 1 m/s in a standard atmosphere (23°C, 1023 hPa).<br />
In order to be able to apply the locomotion mechanism of a fish in water to a deformable<br />
airship in air, the fluiddynamic conditions as well as the geometrical shape of fish and airship have to<br />
be similar. In general, two scenarios are fluid dynamically similar, if - strictly speaking - all the<br />
following non-dimensional parameters are equal:<br />
(a) Reynolds number<br />
(b) Mach number<br />
(c) Strouhal number<br />
(d) Froude number<br />
However, in a specific case it is not important, that all of these parameters are exactly equal.<br />
Therefore a ranking of the importance of these parameters has to be made. The Froude number<br />
correlates the inertial with gravitational forces, e.g. this number must be considered in cases, where<br />
gravitational forces are significant. We can ignore this number, because we are considering here<br />
primarily horizontal swimming and flying. What Mach number is concerned, we have to consider the<br />
flight speed compared to the speed of sound. Because the flight speed of the airship is very small<br />
compared to the speed of sound, it means firstly, that the Mach number will be close to zero and<br />
secondly, that the surrounding air flow can be assumed to be incompressible. The ratio of inertial to<br />
viscous forces is known as the Reynolds number. If the Reynolds number is low (less than 10 3 )<br />
viscous forces are large compared to inertial forces and therefore inertial forces can be neglected. If<br />
the Reynolds number is large (larger than 10 6 ) viscous forces are small compared to inertial forces<br />
and therefore viscous forces can be neglected. It will be calculated here with respect to the whole<br />
body length:<br />
1.<br />
0<br />
Re <br />
16.<br />
6 10<br />
6<br />
u 0L<br />
1<br />
6 0.<br />
36 10<br />
(3)<br />
6
Hence, none of the two conditions mentioned above are satisfied. Therefore it can be<br />
concluded that the viscous forces are of the same order of magnitude as the inertial forces. One<br />
condition of similarity is thus, that the Reynolds number must be equal.<br />
The Strouhal number is the ratio of the forces due to unsteady flow and forces due to steady<br />
flow. Obviously this is the non-dimensional parameter which plays the major role for the fluid<br />
dynamical similarity in our case. The Strouhal number is defined as:<br />
St<br />
u<br />
Df<br />
(4)<br />
0<br />
Where D is a typical dimension of the vortex street generated in the wake of the body, f is the<br />
stroke frequency and u0 is the cruising speed of the object. Because D is not an a priory known value,<br />
usually the Strouhal number is calculated with the peak-to-peak stroke amplitude of a reference point<br />
(the trailing edge of the tail fin) instead of D. Other definitions have also been used, such as the depth<br />
of the tail fin [16], or even the full length of the fish [11]. Following Triantafyllou [17] we will us the<br />
Strouhal number based on the peak-to-peak amplitude, 2a:<br />
2af<br />
St' (5)<br />
u<br />
0<br />
The importance of the Strouhal number in efficient swimming of fish has been reported in<br />
numerous studies, see for example [18-21].<br />
2-3. The trout as a model for a 6 meter long airship<br />
From the various fishes we want to find one, which would be a meaningful model for our<br />
airship. In a first step we will focus on fluiddynamic aspects and ignore restrictions due to aerostatic<br />
or due to the structural set-up. Considering the fluiddynamic similarity, the first requirement is a<br />
Reynolds number of 0.36·10 6 . Nägele has collected fluiddynamic data of various species in water [21]<br />
and we found for example the tuna and the rainbow trout, which are swimming with such a Reynolds<br />
number. This can be seen by the following calculation for the trout: The trout is 0.3 m long, and<br />
reaches a steady state swimming speed in water of 1.2 m/s. With L = 0.3 m, v∞ is 1.2 m/s, and ρ is<br />
1.0·10 3 kg/m3 and μ is 1.002·10 -3 kg/ms for water, the Reynolds number is:<br />
1.<br />
0 10<br />
Re <br />
1.<br />
002 10<br />
3<br />
u 0L<br />
1.<br />
2 0.<br />
3<br />
3<br />
6<br />
0.<br />
36 10<br />
(6)<br />
Both are very efficient swimmers. Looking at the fish geometry as a design model for a<br />
deformable airship, the rainbow trout seems to be a promising shape for the airship because of its<br />
laminar formed body. Additionally, the efficient propulsion is combined with a good manoeuvrability,<br />
which also important for airships. On the other hand the tuna has an even more efficient lift-based<br />
propulsion mechanism compared to the trout, with a minimized tendency to side slipping and yawing<br />
of anterior body due to inertial recoil. However this fish is known to have a low efficiency at low<br />
speeds and bad manoeuvrability. Therefore we decided to use the rainbow trout as a design model for
further studies on our airship design.<br />
The shape of a rainbow trout has a width-to-body length ratio of approx 14% and a<br />
height-to-body length ratio of approx. 22%, see Fig. 4. [11]. The maximum width and height is at<br />
40% of the body length. Analytically, this shape can be approximated by a NACA0014-Profil in the<br />
x-y plane and NACA0022 in the x-z-plane. Such shapes are known to have very low drag coefficients.<br />
The body cross section can be assumed to be elliptical. In this way, we can take the trout as a model<br />
for the undeformed shape of the airship.<br />
If we follow the paradigm of biomimetic, e.g. that nature has found not only optimized forms<br />
but also the corresponding optimized motion pattern [22], we can choose the motion pattern of the<br />
trout also for our airship in air. The wake of a rainbow trout has been studied using stereoscopic<br />
digital particle image velocimetry [23]. The motion pattern of a trout has been measured for example<br />
by Webb [24]. The lateral amplitude increases along the fish from head to tail. Interestingly the<br />
amplitude is not zero at the forward and middle part of the body. The propulsive elements near the tail<br />
have a much larger thrust component due to greater traverse distance and larger speed which results<br />
in more water acceleration. Additionally, the propulsive elements are oriented more toward the fish<br />
swimming direction in the aft part [25].<br />
Figure 4. Typical undeformed shape of a trout [11].<br />
If we analyze the body motion of the steady state swimming we find the following typical<br />
values: The amplitude of the fin stroke is 20% of the length. The stroke frequency f is 4.5 Hz and the<br />
resulting swimming speed u0 is 1.2 m/s. With these values we find a Strouhal number of 0.45. A<br />
polynomial function representing the increasing lateral amplitude from the head to the tail can be<br />
defined, see for example Webb [24]. For simplicity in our case we used a quadratic function as a first<br />
order approximation. Therewith the caudal fin stroke frequency is exemplarily calculated: With St’ =<br />
0.45, a = 20% of 6 m = 1.2 m and u0 = 1 m/s. The stroke frequency is:<br />
St'u<br />
0 0.<br />
45 1<br />
f 0.<br />
1875 0.<br />
2Hz<br />
(7)<br />
2a<br />
2 1.<br />
2<br />
The adaptation of the fish-like locomotion mechanism in water to a deformable airship in air<br />
should be possible, if these geometrical and fluid dynamical similarities are satisfied. The Reynolds<br />
number with respect to body length and the Strouhal number are the non-dimensional parameters of<br />
relevance to meet fluid dynamical similarity. Therefore we can conclude that a full grown rainbow<br />
trout is a meaningful design model for the deformable airship.
2-4. The Structural Concept of the biomimetic airship<br />
The structural concept of a deformable airship is a highly multidisciplinary challenge. In<br />
contrast to the trout in water, an airship has to compensate its weight with the aerostatic lift produced<br />
by a lighter-than-air gas. The requirement of buoyancy does not allow slender shapes, because they<br />
have a small volume-to-surface ratio, which reduces the payload capacity. This is in direct contrast to<br />
the requirement of maximum speed and efficiency, which is better the more slender the body is. In<br />
addition in airship design the shape of the body can not be chosen free from structural restrictions. In<br />
case of a rigid airship the structural weight is much larger than the hull weight. Therefore for smaller<br />
airship this approach is not feasible and a non-rigid design is favourable. In case of non-rigid airships,<br />
the shape is defined by the hull geometry and the internal pressure. If we consider further the<br />
undulatoric propulsion mechanism we have to increase lateral area in order to have enough contact<br />
area between the body and the fluid. One possibility is to have a height-to-width ratio of 3 – 4, seen in<br />
Fig. 4 or to add fins in the symmetry plane, shown in Fig 16. Finally all the requirements mentioned<br />
above have to be fulfilled in one design.<br />
Figure 5. Design concept of the biomimetic airship.<br />
Our design concept is a balanced compromise between these requirements. The basic<br />
dimensions are a total length of 6.6m, the maximum height is 1.9m and the width is 1.5m, see Fig. 5.<br />
It consists of a pressurized body with an internal rigid multi-body structure in the symmetry plane.<br />
This structure elongates the cross sections in the vertical direction, which results in a larger height<br />
than width. The body is flexible in the symmetry plane at least at one cross-section. At this position an<br />
active body segment allows to bend the pressurized body of the body actively. A first estimation of<br />
the weights and the balance of this design proposal is given in Table 1.<br />
The tail-fin is a compliant non-pressurized flat plate with Fin Ray Effect. The Fin Ray<br />
Effect has been found in tail fins of fishes by Leif Kniese [26]. The kinematic of such a structure<br />
allows a strong interaction of the structure with the fluid. The importance of flexibility of fins for<br />
propulsion has been reported for example in [27]. In case of a structure with Fin Ray Effect, the<br />
combination of the lateral pressure distribution and the forces introduced as a pair at the root of the fin<br />
results in large S-shaped deflections of the whole fin, see Fig. 6. The activation of the tail fin has in<br />
principle three degrees of freedom: the first one is a flapping motion (translative motion) of the root,<br />
the second one is a rotation of the root and the third one is the activation of the Fin Ray Effect,<br />
which results, in a variation of the S-shape of the fin. In our case due to simplification we will only<br />
activate two of them: The translative motion and either the rotational motion or Fin Ray Effect <br />
(The decision will be made based on wind tunnel tests). The translative motion will be realized by the<br />
bending motion of the active body segment (described in detail in section 3.1). The second motion<br />
will be realized by the actuator module located between the body and the fin (green box in Fig. 5, see
also section 3.2).<br />
Table 1. Estimation of weights and balance for the proposed biomimetic airship design.<br />
Component Structural weight Position from tip<br />
Passive envelope 513 g 250 mm<br />
Active material in the<br />
envelope<br />
260 g 375 mm<br />
Internal structure 1750g 250 mm<br />
Gondola, with engines,<br />
electronics<br />
2150g 60 mm<br />
Activation module for the<br />
tail fin<br />
650g 511 mm<br />
Tail fin 590g 640 mm<br />
Payload and trim weight 200 g 60 mm<br />
Total weight<br />
(= aerostatic lift)<br />
6120 g 250mm<br />
The actuation technology necessary in order to get the body deformation described above will<br />
be obtained through the application of Dielectric Elastomer (DE) membrane actuators. Dielectric<br />
Elastomers are one material class of Electroactive Polymers (EAPs) and are promising material<br />
systems as actuators in active structures, where large deformations are required. They transform<br />
electrical energy directly to mechanical work and produce large strains (20% and more). Especially<br />
Dielectric Elastomers were shown to have good overall performances. Pressures of 16.2 MPa, free<br />
area strains of 215% and specific elastic energy densities of 3.4 J/g could be shown [28].<br />
A DE actuator is basically a compliant capacitor, where a passive elastomer film is<br />
sandwiched between two compliant electrodes. When an electrical voltage is applied, the<br />
electrostatic forces arising from the charge displacement on the electrodes squeeze the elastomer film.<br />
This electrode pressure mechanically loads the polymer film. Because such elastomers are essentially<br />
incompressible the area of the capacitor is enlarged. As soon as the voltage is switched off and the<br />
electrodes are short-circuited the capacitor contracts back to its original shape.<br />
With this technology membrane- or shell-like structures can be created witch integrated<br />
actuator and load-carrying functionality. The electro mechanical behaviour of a functional model of<br />
an “active envelope” was studied, [29]. An active envelope is the combination of such a DE<br />
membrane actuator mounted on an airship envelope. Mechanically it is a multilayer membrane, with<br />
a lightweight and helium-tight membrane, which is characterized by a high tensile strength and a high<br />
compressive compliance, and a DE-actuator consisting of at least one prestretched dielectric film<br />
layer coated on both sides with compliant electrodes. The basic idea of this structural element is<br />
illustrated schematically in a force-versus-deformation diagram, see Fig. 8.a. During the<br />
manufacturing process the over-stretched DE-actuator is attached directly to the tight airship<br />
envelope (point 1). If the actuator exerts a resulting tension force larger than that induced by the<br />
internal pressure in the envelope, the membrane below the DE-actuator will wrinkle (from point 1 to<br />
2 on the line denoted as “passive DE”). By applying an electrical voltage to the DE-actuator, the DE<br />
actuator is enlarged and the envelope segment regains its fully elongated state (point 3 on the line<br />
denoted as “active DE”). The slope of both lines represents the stiffness of the DE actuator. If the<br />
internal pressure is too high, then the envelope is always tight and the stiffness of the system is the<br />
stiffness of the envelope (steep lines beyond point 1).Therefore it is important to justify the internal<br />
pressure such that the full deformation range (difference between point 2 and 3) is possible.
Figure 6. Demonstration of the Fin Ray Effect.<br />
In a theoretical study the membrane stresses and strains of such an “active envelope” for an airship<br />
body slightly pressurized and deforming like a trout have been analyzed. In order to experimentally<br />
simulate the stress state of the airship envelope, a functional model of the active envelope was defined<br />
and experimentally characterized. With this cruciform planar functional model mounted on an<br />
in-house made testing device the deformations on activation under representative membrane stresses<br />
could be measured, see Fig. 8.b. Therewith the feasibility of the proposed concept could be<br />
investigated. The line loads on each arm of the cross were determined to represent the stress<br />
distribution in the slightly pressurized (300 Pa) airship. These line loads were calculated for a 6m x<br />
3m x 1m elliptically shaped body. The line loads vary with orientation and location from 160 N/m in<br />
the longitudinal direction at the thickest section to zero at the nose and the tail. The circumferential<br />
line load varies from 80 N/m to zero respectively. The ratio between longitudinal and circumferential<br />
line loads is between 1 and 2. Furthermore, the envelope strain and strain rate requirements for steady<br />
(and accelerated) swimming were also defined. The required local deformations of the envelope were<br />
derived from the analysis of the deformed fish body. The maximum strain of the steady state<br />
swimming mode was 15.1% in longitudinal direction.<br />
Figure 7. : Schematic of deformed shape of an airship, mimicking the motion of the fish body
The envelope material Nonex® (detailed description, see below) satisfied the basic mechanical and<br />
aerostatic requirements. Thanks to its small thickness (25 μm), it can be wrinkled easily. The metal<br />
coating grantees the required Helium tightness. The envelope can be cut in segments that are<br />
successively welded together in order to achieve a Helium-tight body with high compliance under<br />
compression forces.<br />
The largest longitudinal activation strain was achieved by the active envelope with a (6.5,<br />
3)-over-stretched DE-actuator. It reached 13.5% at an activation voltage of 3.5kV. This was reached<br />
under a biaxial line load ratio of 2.37. The strain could even be increased through a higher electrical<br />
activation voltage. An extrapolation of the measured data results in an activation strain of 16% at<br />
approx. 3.8kV, which satisfies the lateral strain requirement of 15.1% for steady swimming.<br />
Furthermore, the reduction of the transversal load not only allows to increase the longitudinal<br />
activation strain, but also to decrease the line load ratio from 2.37 to 2. Thus, the requirement for the<br />
airship line load ratio could be fulfilled. The membrane line load requirement of 160 N/m at Δp = 300<br />
Pa and 80N/m can be fulfilled through the stacking of eight DE-actuators. These experimental results<br />
allow concluding that the proposed concept for an active envelope is feasible at least for the steady<br />
swimming mode.<br />
Figure 8.a. Force versus displacement behaviour of an<br />
active segment of the envelope.<br />
2-5. Computational Flow Simulations<br />
Figure 8.b. Biaxial tension test set-up for the active<br />
segment of the envelope.<br />
Based on the methodology developed in reverse engineering of self-propelled anguilliform<br />
swimmers [22], the fish-like motion has been simulated with a simplified geometrical representation<br />
of the design proposal. The lens or plate formed cross-sections of the original body have been<br />
transferred into elliptical shapes. The motion has been parameterized as a wave of curvature <br />
travelling along the centreline of the body:<br />
s, t<br />
ssin2(<br />
t / T ( s)<br />
<br />
<br />
(8)<br />
Where K(s) is the curvature amplitude, which is modulated by a sine-wave with period T and<br />
phase shift (s). With these parameterization continuous deformations of the body, discrete hinges, as<br />
well as active or passive tail fin deformations can be modelled effectively. As a reference case K(s)<br />
and (s) were chosen to represent the motion pattern of a trout in steady state swimming, as described
in section 2.3.<br />
The system of the deforming body interacting with the surrounding fluid is described by the<br />
3D incompressible Navier-Stokes (NS) equations that are coupled to Newton’s equations of motion<br />
for the self-propelled body. The NS equations are solved using the Finite Volume package STAR-CD<br />
v. 3.15 extended with user subroutines for the fluid-body coupling [22].<br />
The current approach allows calculations at a maximum ReUL of approx. 3000. Note that this<br />
Re number is several orders of magnitude lower than the Re number of the airship. Nevertheless the<br />
computational model can provide valuable information for critical decisions for the design of the<br />
biomimetic airship. An extensive study of this flow is the subject of ongoing work [30] addressing<br />
questions such as: How does a design with discrete hinges compare to a continuously deforming body?<br />
What is the effect of the deflection angle and phase shift of a flexible tail fin on the swimming<br />
performance?<br />
For the case with one discrete hinge and a stiff tail fin the general structure of the wake<br />
remains similar to the results reported in Fig. 9. We find that simplifying the motion with a single<br />
hinge and a stiff tail fin still allows similar swimming speeds if the tail beat amplitude is slightly<br />
increased compared to the case with continuous deformation. Investigations with modelled fin<br />
flexibility show that the highest efficiency is achieved when the fin bending has a phase lag of<br />
roughly pi/2.<br />
Figure 9. Vorticity iso-surfaces coloured with span wise vorticity of the trout motion pattern.<br />
3. PRACTICAL FEASABILITY – RESULTS OF DEVELOPMENT TESTS<br />
In the second part of the work the structural elements of the biomimetic airship with a fish-like<br />
propulsion system were developed. The following parts of the development are completed:<br />
1) An active body segment<br />
2) Active hinge for the actuation of the tail fin<br />
3) Design of a tail fin with Fin Ray Effect<br />
In the following sections the results of these studies will be summarized.<br />
3-1. The active body segment<br />
The goal of this work package was to develop and characterize an active body-segment based<br />
on DE membrane actuators. Based on the feasibility study on the active envelope, [29], the next step<br />
was to build a pair of actuators positioned at each side of the pressurized body, see Fig. 10.a. For that<br />
purpose slightly curved prestretched VHB-4910 actuators were mounted on a framework and<br />
activated alternately, see Fig. 10.b. In this approach the actuators are separated from the airship<br />
envelope to avoid undesirable friction between the envelope and the actuator. To characterize the<br />
active body-segment a test stand has been built-up. Dynamic measurements of the angle and static<br />
measurements of the force are taken of a single-layer and a double-layer functional model at various
frequencies. The single-layer prototype reached 13°, which is 90% of the required 14.5° deflection<br />
angle. By optimizing the electrical supply and reduction of friction in the hinge of the framework we<br />
expect to reach the required deflection angels.<br />
Figure 10.a. Schematic of the active body segment, with<br />
two pressurized half-bodies (white), the internal rigid<br />
structure (red), the pivot line (arrow) and the membrane<br />
actuators on each side (black dashed).<br />
3-2. The activation of the tail fin<br />
Figure 10. b.A single-layer membrane actuator in the test<br />
rig (black: active area)<br />
In a second study the module for the activation of the tail fin (schematically represented by the<br />
green box in Fig. 5) was developed. In an earlier work a so called active hinge has been developed<br />
successfully for the activation of steering rudders, [31, 32]. Based on these results the next<br />
development step was to scale-up this design in order to increase the forces. A theoretical simulation<br />
tool has been used to define the dimensions and the shape of it. In order to define the required forces<br />
the aerodynamic loads on a flapping fin were estimated. The significantly non-stationary flow<br />
condition of a flapping fin was experimentally simulated by a rotation of a plate and measuring the<br />
moment needed for this movement and the calculation of the drag force of the same plate hold<br />
perpendicular to a stationary flow. On the other hand the force and moments of wind tunnel tests (see<br />
section 3.3) were also taken into consideration. The required activation moment at the hinge was<br />
found to be in the range of 1.75 to 3.0 [Nm]. Finally the dimensions of the active hinge were chosen to<br />
be 1m high, and 30cm deep with 4 layers of VHB-4910 DE membranes on each side, see Fig. 11. The<br />
active area on both sides was reinforced by thin carbon rods in order to hold the prestraining of the<br />
acrylic film in the vertical direction. In order to characterizing the electro-mechanical behaviour of<br />
this module, a test bed was built-up, where aerodynamic loads were simulated by two linear springs<br />
generating an external load linearly increasing with the deflection angle. Measured electrical signals<br />
(current and voltage) and the mechanical behaviour of the springs allowed defining the power<br />
consumption, the mechanical work done per activation half-cycle as well as the efficiency. A<br />
maximum hinge moment of 1.25 [Nm] at 20° deflection and 0.2 Hz was reached. This actuator allows<br />
generating 0.14W mechanical power. The results, which were realized, could meet in principle the<br />
requirements. The uncertainty in the assumption of the aerodynamic loads is not a critical point,<br />
because the forces generated can be scaled in the final design by the number of DE membrane layers<br />
on each side.
Figure 11. Full size functional model of the active hinge for the activation of the tail fin.<br />
3-3. The aero-elastic tail fin<br />
There is only a limited number of projects on oscillating foils or fins and to the knowledge of<br />
the authors they have been done all in water, see for example [33] and [34]. We have studied the<br />
design of an aero-elastic tail fin as an element of the undulatoric propulsion. Again with the theory of<br />
similarity it can be shown, that an elastic tail fin of such a 6 meter long airship is similar to a tail of a<br />
trout in water, if the dimensions of the fin and the deformation is geometrically similar. In Fig. 12<br />
three tail fins are shown witch are technical simplifications of the natural model of a trout.<br />
Fin A represents the tail fin of a trout (depth =0.175L, height = 0.35L, where L is the total<br />
length of the trout). Fin B represents the aft part of the body plus the tail (depth =0.36L, height =<br />
0.41L). Both fins were fabricated as partly stiffened Depron-plate (thickness 5 mm and 9mm<br />
respectively). Fin C was a Fin with Fin Ray Effect shaped like the natural tail fin. It was made from<br />
a carbon tube framework with a textile skin (depth =0.175L, height = 0.29L).
Figure 12. Shape and size of three tail fin design, tested in the wind tunnel.<br />
A first series of wind tunnel tests have been performed, where these tree fins have been<br />
oscillating around a rod mounted on a 6 degree of freedom load cell (the scaling parameters are given<br />
in Table 2). The rod could be moved translative and in rotation independently. With this unique<br />
apparatus a fish-like motion could be generated. In these tests the translative and rotational amplitude,<br />
the frequency and phase shift as well as wind speed were varied systematically. The movement of the<br />
fin and the flow in the wake of it were monitored with a high-speed video camera. Based on the force<br />
and moment measurements with the load cell, the dimensionless propulsion or drag forces and the<br />
propulsion efficiency could be evaluated.<br />
By analysing the high speed camera video streams, (see Fig. 13) both Strouhal numbers<br />
(defined in eq. 4 and 5) could be determined. The tests show, that only above a critical frequency of<br />
approx. 1 Hz propulsion is produced by the oscillating fin. The critical frequency is dependent on the<br />
type of fin (see Fig. 14), the ratio between translative and rotational movement and the phase shift<br />
between them (see Fig. 15.). The maximum of propulsion has been found with Fin C at maximum<br />
frequency of 2 Hz. However the best efficiency was found to be 23% at a frequency of 1.13 Hz with<br />
Fin B. The phase shift between translative and rotational movement has also a large influence on the<br />
propulsion. An optimum is found close to 72° also reported by Hertel [11].<br />
In this first test series the Fin Ray Effect in Fin C was not yet activated. In a second test<br />
series the Fin Ray Effect on propulsion force and efficiency will be explored in detail.<br />
3-4. Functional models<br />
With a model airship (Fig. 16) the undulatoric propulsion in air has been explored. The airship<br />
envelope was made of Nonex®, which is a polymeric multilayer structure especially developed for<br />
Lighter-than-Air vehicles.<br />
This functional model was developed in order to verifying the practical feasibility of the<br />
undulatoric propulsion concept in air. While the wind tunnel tests gave first results on possible<br />
designs of fins and their performances the practical feasibility was still an open task. There are only a<br />
very limited number of airships that are propelled by a fish-like propulsion system: One is the<br />
“Air_ray” from FESTO, [35]. This free-flying object was a semi-rigid hybrid airship, with a lifting<br />
body filled with Helium in the centre section and flapping wings on each side. This airship was<br />
looking like and mimicking successfully the motion of a stingray. It was first shown at the
“Hannovermesse” in Hannover in 2007. Another one is a model blimp called “Wanda” shown by<br />
Martin Müller at the Wall-Halla indoor flying meeting 2008, [36]. However, none of these objects<br />
have been investigated scientifically.<br />
Table 2. Scaling of the fin for the wind tunnel (typical numbers of the trout in water and design point of the model in the<br />
wind tunnel).<br />
Parameter Unit Trout Model<br />
Fluid water air<br />
Kinematic<br />
viscosity<br />
Total length of<br />
fish / airship<br />
ν<br />
[m 2 /s]<br />
10 -6 1,6·10 -5<br />
L [m] 0.3 1.72<br />
Reynolds number Re 0.36·10 6 1.60·10 6<br />
Fin length l [m] 0.075 0.3<br />
Flow speed U [m/s] 1.2 1.5<br />
Strouhal number Str’ 0.45 0.45<br />
Frequency f [Hz] 4.5 1.4<br />
Peak to Peak<br />
amplitude<br />
APP [m] 0.12 0.48<br />
Figure 13. Fin B in the wind tunnel with vortexes generated in the wake (side view).
Our biomimetic airship allowed to exploring scientifically the biomimetic propulsion system<br />
in flight tests. This model was equipped with three different flexible fish-like tail-fins instead of the<br />
cross-tail. One was a small tuna-shaped tail fine adopted from the fish “Scomber Japonicus “, and two<br />
sizes of the trout-like tail fin were tested, see Fig. 16.<br />
trust coefficient c T<br />
trust coefficient c T<br />
3.0<br />
2.5<br />
2.0<br />
1.5<br />
1.0<br />
0.5<br />
0.0<br />
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2<br />
-0.5<br />
-1.0<br />
0.5<br />
0.4<br />
0.3<br />
0.2<br />
0.1<br />
-0.2<br />
-0.3<br />
-0.4<br />
-0.5<br />
Fin A<br />
Fin B<br />
Fin C<br />
Frequency [Hz]<br />
Figure 14. Dimensionless drag/propulsion force versus frequency.<br />
Fin A<br />
0<br />
-84<br />
-0.1<br />
-78 -72 -66 -60<br />
Phase ψ [ °]<br />
Figure 15. Dimensionless drag/propulsion force versus phase shift for fin A at the design point.
Figure 16. Shape and size of the tail-fins tested in flight tests (red: tuna-shaped, green: small trout-shaped (“B20”, “B21”,<br />
“B24”) blue: large trout-shaped “B30”).<br />
“B24” was identical in size and shape as the fin B evaluated in the wind tunnel. The large one<br />
(“B30”) was scaled correctly in respect to the relative size of the tail-fin shown in Fig. 5. These<br />
tail-fins were mounted with a hinge at the end of the body, see Fig. 17. With a conventional servo<br />
motor this tail-fin was driven such that an undulatoric flapping motion of the root of the fin was<br />
realized. Various amplitudes (±12.5°, ±20°, ±30°) and frequencies (0.5 – 2 Hz) could be applied. In<br />
total eight different fins, with different shapes, sizes and stiffness were tested in flight. The flight<br />
motion was qualitatively judged with respect to stability and the cruising speed was measured.<br />
Figure 17. Functional model of a biomimetic airship.<br />
The effect of shape, size and stiffness on the speed of the airship at various frequencies could<br />
be quantified. All of these design parameters have a significant effect on the cruising speed. The<br />
speed is increasing with increasing frequencies (and increasing amplitude) as well as with increasing<br />
stiffness of the tail-fin, sees Fig. 18. A maximum speed of 1.55 m/s could be reached at a Strouhal<br />
number of 0.2.<br />
As Wiguna has reported for fish-swimming in [37], we can also conclude for our biomimetic<br />
airship, that the total area and the aspect ratio have a significant influence on the speed. McHenry [38]<br />
concluded from fish observations, that fish do control their speed by varying their body motion<br />
pattern. In the design of the biomimetic airship the resulting motion pattern is crucial for an optimal<br />
speed. Therefore the stiffness of the fin plays an important role in the design of a biomimetic airship.
[m/s]<br />
1.70<br />
1.50<br />
1.30<br />
1.10<br />
0.90<br />
0.70<br />
0.50<br />
B30<br />
B20<br />
B21<br />
B24<br />
0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80<br />
[Hz]<br />
Figure 18. Cruising speed versus flapping frequency for different sizes and stiffnesses of trout-shaped fins: “B30”: large,<br />
moderate stiff fin, “B20” small, low stiff fin, “B21”: small, moderate stiff fin, “B24”: small, high stiff fin.<br />
3-5. Open questions and future work<br />
The major task in the near future will be the structural technology of the active body. Detailed<br />
design studies on structural configurations and the definition of the distribution of active body<br />
segments to generate the required bending deformation have already started. So far the experiments<br />
with semi-rigid bending body segments, the required bending angle could not yet be reached under<br />
standard operational conditions. The manufacturing process for these active segments is still<br />
unsatisfactory. The primarily hand-made active hull segments show still a rather poor reliability and<br />
the reproducibility has to be improved significantly by using industrial fabrication processes.<br />
Due to the fact, that we have not yet the methods available to fully simulate the structural<br />
mechanics and the fluid-dynamics the empirical approach is very important in this project. We will<br />
continue to explore the structural behaviour of active membranes in experiments, as well as the<br />
fluid-dynamic performances of the fins and the whole airship in wind tunnel tests or flight trials.<br />
Optimization of the whole system of a biomimetic airship will be the subject of long-time research,<br />
also in our group.<br />
4. CONCLUSIONS<br />
The proposed concept of a biomimetic airship is a highly multidisciplinary challenge. Many<br />
aspects, such as aerodynamics, aerostatics and structural mechanics have to be fulfilled in order to be<br />
a functional solution. For many of these design criteria the methods have not yet been developed in<br />
detail. However, if there is a combination of active bending body segments, tail fin actuation and<br />
aero-elastic tail fin a more energy efficient, noiseless and environmental friendly transport system<br />
would be possible.
ACKNOWLEDGEMENTS<br />
The flow simulations performed by Manfred Quack, Dr. Stefan Kern and Prof. Petros Koumoutsakos<br />
at the Chair of Computational Science of ETH Zurich are greatly acknowledged.<br />
The support by Dr. Stefano Airaghi in the wind tunnel tests on tail fins at the Institute of<br />
Fluiddynamics at ETH Zurich is greatly acknowledged.<br />
We thank Christian Gephardt from AeroiX GmbH for the design, manufacturing of the various<br />
envelopes and Martin Wähmer from the Institute of Aeronautics and Astronautics, TU Berlin for the<br />
evaluation of the overall performance of the “airfish 3.10” design.<br />
The project has been financed by the board of directors of <strong>Empa</strong>.<br />
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